Troy Deeney and Roberto Pereyra were also on target as Nigel Pearson’s team made it 13 points from their last five games while the Cherries are in freefall and have lost nine of their last 11 Premier League fixtures.
Revitalised Watford were the better team throughout the match and, after a Dan Gosling error had let Ismaila Sarr in, Steve Cook did well to block the 21-year-old Senegal winger’s shot.
When the Cherries responded, Ben Foster kept Harry Wilson’s 30-yard free-kick out, but the visitors continued to have the upper hand and Mark Travers in the Bournemouth goal had to make a smart save to deny Gerard Deulofeu.
Lethargic Bournemouth struggled to create anything from open play and it came as no surprise when the Hornets took the lead two minutes before the break, Doucoure making no mistake as he turned Sarr’s cross home from close range after Travers’ poor clearance.
Eddie Howe’s side were little better after the break and Sarr wasted a good chance to make it 2-0 in the 53rd minute when his weak effort was cleared by Simon Francis before Deulofeu sliced a presentable opportunity wide.
The visitors continued to look dangerous on the counter-attack throughout the second half and, after Nathaniel Chalobah had lashed a long-range shot just over the bar, Watford doubled their lead in the 65th minute when Deeney smashed the ball home after good work by Sarr.
In stoppage time Pereyra added to Bournemouth’s problems with a third goal and the home team’s five-year stay in the Premier League increasingly looks as though it may be coming to an end.